On a backward problem for fractional diffusion equation with Riemann‐Liouville derivative

Abstract

In the present paper, we study the initial inverse problem (backward problem) for a two‐dimensional fractional differential equation with Riemann‐Liouville derivative. Our model is considered in the random noise of the given data. We show that our problem is not well‐posed in the sense of Hadamard. A truncated method is used to construct an approximate function for the solution (called the regularized solution). Furthermore, the error estimate of the regularized solution in L2 and Hτ norms is considered and illustrated by numerical example.